Differentiability with Respect to Initial Data for a Scalar Conservation Law
We linearize a scalar conservation law around an entropy initial datum. The resulting equation is a linear conservation law with discontinuous coefficient, solved in the context of duality solutions, for which existence and uniqueness hold. We interpret these solutions as weak derivatives with respect to the initial data for the nonlinear equation.
KeywordsInitial Data Cauchy Problem Entropy Solution Duality Solution Weak Stability
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